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  1. Namely, is a "constant" E field changing direction at a rate of the applied frequency?

  2. Does the E field in coplanar plates looks like this? Is there a way to derive the Capacitance of this type of capacitor - I have seen a few different equations online.

enter image description here

Source: https://www.comsol.ru/forum/thread/attachment/124523/Planar_capacitive_sensors___designs-24313.pdf

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  • \$\begingroup\$ Sara, why not just write up a Python script in Trinket or Glowscript and just calculate the results. You will need to work out the charge gradients, though, as it goes from parallel-plate and swings open towards a fringe-field sensor (as you show it.) There is also this helpful article which you can use to test your code and make sure it works, well. The article covers some interesting distinguishing results that can be used to good effect, too. \$\endgroup\$
    – jonk
    Oct 24, 2022 at 23:18

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In a parallel-plate capacitor (a), with area much greater than perimeter so as to ignore fringing, dimensional analysis suffices. That is,

$$ C = \epsilon_0 \frac{A}{d} $$

For plate area \$A\$, spacing \$d\$, and \$\epsilon_0 \approx\$ 8.85 pF/m.

The field has the same shape at all non-zero magnitudes and direction is equal to instantaneous applied voltage, so, alternates with AC.

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  • \$\begingroup\$ What about skin effect? would that cause the inner field to lag the outer field? \$\endgroup\$ Oct 26, 2022 at 1:46
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    \$\begingroup\$ @Jasen Locally in the surface of the plates, yes, assuming metals. (No materials have been defined here, so the default assumption is ideal conductors and insulators.) Likewise, a lossy dielectric will have E and D fields slightly out of phase. \$\endgroup\$ Oct 26, 2022 at 2:35

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